In a similar way, amortized communication complexity can be defined for probabilistic version of communication complexity. In general, the properties of amortized randomized communication complexity remains not well understood, though several nontrivial particular examples are known. For instance, in [1]} it was proven that amortized randomized complexity of the equality predicate is only \(O(1)\) , while it is known that for one individual predicate
\(\mathrm {EQ}:\lbrace 0,1\rbrace ^n\times \lbrace 0,1\rbrace ^n\rightarrow \lbrace 0,1\rbrace \)
\(\mathrm {EQ}(x,y) = \left\lbrace \begin{array}{rl}1,&\mbox{if }x=y,\\0,&\mbox{if }x\ne y\end{array}\right.\) 
